/*
  Copyright 2022 by Sean Luke and George Mason University
  Licensed under the Academic Free License version 3.0
  See the file "LICENSE" for more information
*/

package sim.util;

/** 
    An implementation of Kahan summing, which is more accurate than just adding numbers together.
    You can either create a Kahan object and little by little sum into it.  You can also just
    pass an array of doubles to sum() to build the Kahan sum and immediately return it.
*/
        
public class Kahan
    {
    double sum = 0;
    double comp = 0;
        
    /** Clears the sum. */
    public void clear()
        {
        sum = 0;
        comp = 0;
        }
                
    /** Adds val into the sum.  Returns the sum result. */
    public double add(double val)
        {
        double y = val - comp;
        double t = sum + y;
        comp = t - sum - y;
        sum = t;
        return sum;
        }

    /** Adds vals into the sum.  Returns the sum result. */
    public double add(double[] vals)
        {
        int len = vals.length;
        for(int i = 0; i < len; i++)
            {
            double y = vals[i] - comp;
            double t = sum + y;
            comp = t - sum - y;
            sum = t;
            }
        return sum;
        }
                
    /** Returns the current sum result. */
    public double getSum()
        {
        return sum;
        }

    /** Produces a Kahan sum of the given vals and returns it. */
    public static double kahanSum(double[] vals)
        {
        double sum = 0;
        double comp = 0;
        int len = vals.length;
        for(int i = 0; i < len; i++)
            {
            double y = vals[i] - comp;
            double t = sum + y;
            comp = t - sum - y;
            sum = t;
            }
        return sum;
        }
        
    static final double[] test = new double[]
    {
    0.4132287435195573, 9.468058454219925, 88.0605482251606, 261.5584851373682, 6059.0900199754005, 38477.104593074044, 362308.405258673, 9916467.824382687, 8808728.907213725,
    0.506176633049291, 3.838870904524203, 78.38826996563316, 600.8673439356406, 5569.7471333725825, 47693.73640049666, 958694.1256212341, 279279.1000149253, 4.311594709066239E7,
    0.18769949569312527, 0.1834087710322596, 3.623501417173647, 606.2050847099996, 9563.706378315997, 45202.96718103615, 644737.2850654569, 1539552.520314943, 7560000.307440407,
    0.5627240525092939, 6.106016728700968, 49.60628208168316, 874.0708417309548, 1512.5138652809333, 51180.39313176736, 945147.020605471, 8384573.932811283, 9.685039556413825E7,
    0.8003964760165333, 1.0115739947421676, 86.0676206726524, 77.9764597781082, 9025.338952424108, 85700.31138021937, 177235.24252680579, 6585777.159095486, 6.493444427868304E7,
    0.10832648023945068, 8.536164104838011, 32.15998961662391, 936.9931252857189, 2593.706850058075, 85901.0181348283, 715923.0649998265, 5347904.904609506, 2.702111534991757E7,
    0.8753536367572385, 0.5197939681070529, 38.695840960615236, 300.1906228334199, 9895.062990024104, 18769.551453307464, 586672.4265224336, 9682185.521864066, 3.285305491247752E7,
    0.08857760987386754, 4.4025776821576335, 87.26654056611123, 515.4268443370258, 7992.987215552048, 68492.40720984047, 291902.83124644036, 5463060.337217156, 5.4559330711016215E7,
    0.9751816245410442, 9.211111370550979, 31.986457144899163, 222.95918388358405, 2110.8984363251348, 9179.580681937337, 586160.5379865002, 3226124.9620719925, 1.4574612986226598E7,
    0.16752471321168838, 5.240720225626751, 29.53365749724618, 979.9319743968023, 7127.1868494268965, 50545.14652493689, 460310.8102478438, 3285896.154836009, 5.908977030837922E7,
    0.8588727313631576, 8.287010614878854, 2.68117399877259, 364.6058513666789, 6070.006533421404, 63073.842993942344, 732283.7323569921, 2413080.4875979484, 2.1899503409833223E7,
    0.9102085779788329, 1.7662578745593605, 33.78722491436965, 392.99468763274905, 2817.1878308033447, 21984.045417783393, 220820.8165952591, 7636092.407161795, 8.338057818146347E7,
    0.570078820456342, 5.203553677380874, 21.547945826457216, 204.8922545584483, 1451.9588527723604, 91322.9322730132, 176349.90550544305, 592953.7220277048, 5.7307422435580134E7,
    0.9228632436579163, 8.61730211193092, 54.693614390100855, 254.4525634189968, 7946.6772193086435, 94810.4076165866, 843093.4592042108, 7450032.652867634, 1.7035959321287252E7,
    0.5627783761400523, 5.334922005279701, 95.26613254859294, 407.12665906161396, 7958.468807965987, 43521.00614411584, 791714.7376568592, 1658175.7425704268, 1.6337639870591424E7,
    0.425332847068599, 4.86923882271281, 32.69027219466466, 580.8058607201616, 9869.838894231401, 67894.59548730846, 383773.00694827375, 4416816.436939321, 4.7629750284967065E7,
    0.8465974460313735, 2.100134513903021, 33.92350435521247, 564.1030221775246, 3319.963095900572, 50060.878135081824, 816941.0662732336, 9125301.104645068, 4.3138268367507294E7,
    0.24660883338115247, 2.8908015698330667, 90.94421498226784, 597.4249613426675, 3186.013191658883, 93345.73231534513, 202549.24027828293, 7880763.019933142, 6.0641058966246456E7,
    0.9258162235538138, 8.502482207378327, 39.25535276953156, 190.76054174532774, 8591.181321569997, 13768.189813059094, 966769.3068362914, 7072106.908844946, 5.707388698304978E7,
    0.494205382034714, 2.1855525481166795, 40.349462145496204, 886.7696790214162, 4923.924632447516, 29727.232459792664, 388460.04344227805, 9849902.251887035, 6.089105378949477E7,
    0.46291190865557597, 2.241305289585791, 17.671563394869803, 284.0376953403452, 6365.493780925119, 32197.8781665021, 912601.2576999455, 8292908.689637016, 1.6701955725328466E7,
    0.5703219440617446, 7.28622822603215, 90.15795732345858, 387.940976191918, 2418.195709461749, 66583.11913583861, 587494.495802553, 1847244.7777699297, 5.083755203346636E7,
    0.42111492781061455, 6.227864941470708, 84.29582296832334, 825.3147052797893, 1160.8577019136967, 90978.53986240436, 907570.619650216, 375268.8488877687, 1.0733548272613702E7,
    0.28945493126965993, 6.464288154623164, 30.7338814574154, 703.6952295537192, 4749.741860928386, 98253.9581763527, 867197.6839012684, 47612.11349790795, 1.601820117607905E7,
    0.43577641956674296, 1.5981792795542593, 32.983344957840956, 578.9156689537637, 6980.646765621627, 14426.463057908024, 867547.237927126, 2102207.774498531, 9.55214652526987E7,
    0.4185165370688969, 2.438594416559674, 89.96044661931869, 964.1000018411646, 3373.722461362195, 67968.51987613166, 397949.22371028987, 1956367.1736202347, 4.891336216574343E7,
    0.2893624715518547, 2.0740023279336772, 6.202608555895983, 735.320138717247, 8572.557258212242, 66748.42603888463, 360982.218578967, 5147391.398637206, 1.2219202218825253E7,
    0.4149133270043095, 5.901731660660881, 26.655629477389333, 198.05614940663673, 7069.720702292516, 71186.21913372577, 636581.878480598, 2637538.624466007, 6.110825136433181E7,
    0.2807433228826869, 5.968076078073027, 6.688531393845166, 732.085882017886, 5872.2377638991165, 73030.04412676254, 102853.59638066016, 9739756.778089935, 6.139128705987299E7,
    0.7118787986078856, 5.547660337600321, 81.42625072298412, 154.83558270944286, 4495.680097878344, 20936.862392032806, 706845.0933657957, 4048961.4907424697, 4.4265115307095446E7,
    0.6003870159622767, 5.232090224813843, 69.13752304662005, 659.2027368391782, 5730.300886216506, 39196.81833330074, 789751.9809524866, 6393120.60356773, 3.1204509749359977E7,
    0.9032106410934198, 4.429000045080195, 58.97743547805933, 630.5959745112592, 4068.052792813307, 28571.408612544226, 951846.8892318995, 9783694.522040086, 5277099.960977505,
    0.3664823419769272, 2.957390301905247, 19.46964432929378, 297.0055031354574, 8518.26582603673, 42382.42226133585, 506108.5331280861, 8271163.719614781, 3.037907638368369E7,
    0.2491329950037705, 6.476329092406728, 25.079192830856055, 125.66607949667663, 3565.059658007802, 27326.135350200588, 433094.9253621428, 3873982.496194536, 1.5085662048604298E7,
    0.013411875990670286, 0.6925765765710878, 26.193123078542524, 150.31316215352618, 6358.3440081060435, 93600.20165355719, 730598.5236012937, 2915800.527879744, 7.712949804026245E7,
    0.2771034610918892, 0.4868147166015713, 8.067921796245624, 576.5050497521613, 9478.633054623642, 70151.22144661377, 44301.770964157775, 5241462.751533051, 2.6834884130163983E7,
    0.22700561984052203, 2.1532149693322444, 23.347304408839765, 16.706349970511237, 3322.636323373005, 32059.102973675745, 884858.336793779, 6315472.37480402, 1.8990220521220468E7,
    0.9299626805569555, 2.9778135285159113, 48.63525105108306, 664.0096558474633, 725.4585336308672, 19413.791055836606, 49037.16845976735, 4861522.921535095, 7.295330261485426E7,
    0.5173873524781349, 8.462598507939678, 7.860186801122104, 172.49743112797555, 9329.330437350956, 41476.00176865531, 804966.2481040973, 3318847.772673871, 7.962657371979846E7,
    0.840948751871101, 9.176633665128623, 25.24925286662638, 942.7822624235715, 651.760453802378, 36718.57964440666, 221050.22337927017, 6268246.084382187, 8.585412010065636E7,
    0.9398612456135089, 3.355847432844995, 81.73675870278171, 267.80985930191605, 8988.223080466669, 12707.431329688834, 843915.5867766142, 3679451.078460718, 4.1715613803722575E7,
    0.3409663143447269, 0.7855226168497587, 36.195646008252865, 612.7129750466422, 1394.5316279555075, 93871.949406101, 424214.9743072172, 9208101.493163556, 7.949714733416352E7,
    1.846875036346507E-4, 1.9607914469618815, 87.40757541322674, 411.2100687467279, 4207.888292099707, 51161.99652221114, 97934.31218536841, 3299824.263377621, 1.9294968068180274E7,
    0.7564307044013213, 4.757445515397198, 66.06395431515017, 966.528190429748, 2439.5074341174327, 98935.67668436114, 803269.6909955072, 3135483.293114796, 1.3142886545932498E7,
    0.6988658425316578, 9.277514935066671, 34.23938599124783, 691.5965409050308, 6895.930256442453, 11779.76201003208, 511487.78600667923, 2063173.7170055143, 5.8483792186716035E7,
    0.29244604053379875, 3.410939794220914, 35.49232115839369, 399.69963978846357, 770.2655814234705, 47676.20689961684, 732644.1713373803, 942741.3450709577, 5.114506750209308E7,
    0.2190704955799656, 0.5348392323214901, 17.379227640499227, 855.7426789177233, 2017.0527587301347, 66708.74439925233, 78771.26071033302, 7810508.781065189, 3.735439381783567E7,
    0.2505937334575896, 9.100096651549975, 91.89472710917768, 820.298498709029, 9241.6125071728, 24126.426320382878, 82645.46717108012, 2474025.456097626, 5.8279899966110036E7,
    0.3867045643034299, 4.708358267813302, 13.821143494428977, 937.3317590347315, 5107.488462534874, 81815.77395121071, 700216.8826966378, 6137731.282918908, 3.9464312344054766E7,
    0.765899229089575, 7.168602137277991, 67.3075296791368, 507.1527735485066, 6923.340708484316, 33366.118933813596, 82169.93393705641, 2659936.0653013084, 8.641774607059526E7,
    0.6247625587793446, 9.924097009421956, 2.2137580990621686, 48.96078005931059, 5096.226425111996, 16296.556959337604, 350886.11323844956, 6626974.216993443, 2.194716360852813E7,
    0.5044298648755324, 6.916114152341207, 11.80307160387316, 49.279971208350034, 5118.207531541087, 24232.42845722434, 285126.2695442283, 5733696.106407228, 3.0637915156821426E7,
    0.2857348650360444, 8.808909666660801, 85.14324801896274, 111.99394598519507, 8002.30206096676, 16167.107229598365, 406602.46171656036, 2547874.346163913, 2.922005088118631E7,
    0.5104025571777981, 9.18360840174646, 19.33372905799715, 275.4040237527483, 3812.5650832996294, 64043.713301785276, 662207.6057959858, 7185677.1017991565, 5.9314372420569174E7,
    0.5275008866167316, 7.429062388382822, 8.417926947829535, 148.01156002270622, 9343.221723312341, 56408.116963696295, 289433.7499683528, 5906879.233391588, 5.372115686182666E7,
    0.376714148967877, 0.34555240288697053, 42.409645050218046, 819.9334213156238, 9502.646817090998, 46422.28935230958, 246987.70199157938, 649185.359983706, 5.921632966440399E7,
    0.05458767389058716, 0.909014935517336, 29.54857386705304, 605.7480161818492, 9513.740273051357, 89889.58561984613, 25914.2900052054, 6706832.282480478, 7.23819042132949E7,
    0.2106482340767183, 9.935919671589454, 45.509574996941225, 644.7087392871664, 8968.549360723566, 27109.649744273902, 750107.9539744713, 1585295.9361017381, 2.204252272213091E7,
    0.28595077591963103, 5.5514299920089965, 15.776072300703625, 592.7866750043352, 3119.253713525183, 83632.32290028782, 51590.35496276043, 1406887.8139040263, 9.381440744557387E7,
    0.13047688356798526, 3.8184780609330615, 60.22121018632256, 870.8817105697026, 7737.150554455068, 91769.97064779716, 130260.43956942024, 1778257.7129558995, 2.9623481272890784E7,
    0.7436680717162657, 2.9763408264576507, 74.57065236456492, 443.950616013564, 8447.841380390977, 96985.22469032198, 289582.7897793961, 3627510.3109153807, 8820097.889892243,
    0.740213192389898, 7.257037474999203, 71.26231371921645, 302.3450915982849, 3061.510648368736, 9974.965948233183, 866582.5033956601, 3626949.7249305993, 5.067683285282385E7,
    0.5483871576573501, 8.9329166189857, 80.75328016953847, 738.4933597591329, 9644.580800154781, 72244.54507573174, 527522.8389321667, 1191332.7196774182, 1.3475279416853093E7,
    0.7484470878527103, 4.997283025903021, 8.016140607636702, 124.20255964821104, 1405.9371645291574, 36968.584408091345, 32900.584720857885, 5914580.2242109915, 2.9693584651541814E7,
    0.9244151319294884, 3.763323689107012, 53.82032945255546, 204.1703977658047, 1447.4819986562716, 39258.36405922788, 718188.7839081748, 9473721.54140267, 5.771217728541865E7,
    0.5107115565274315, 5.61847860310651, 25.106382631548474, 222.982843851374, 102.28796144741592, 849.5925193340747, 727070.4854659234, 82161.78206559177, 4.828808979035053E7,
    0.08049268086019057, 4.547990724218383, 16.55099368890667, 274.5081035672304, 3823.820185774813, 62602.917924316316, 539333.500697696, 6883940.622020164, 9.629055402891509E7,
    0.24899661471807577, 9.062093088673697, 94.73245652184548, 138.92000229112412, 3254.96610056624, 89221.85440569809, 783649.3575208916, 9476305.128146198, 4.899287768700917E7,
    0.9651880416259813, 0.5496062204159269, 86.718477804612, 830.6511262080877, 2807.6384295998046, 96757.18033289745, 325556.59908679244, 5017059.972990143, 8.695844861202894E7,
    0.3308014062365996, 3.0377901181391964, 77.69260167580137, 767.024924007238, 7621.354171001349, 3197.106341730804, 398623.317697806, 2074899.6994920555, 9.166640538830967E7,
    0.37523441722531536, 4.295107596461759, 93.1993752408681, 623.7571766138369, 113.78991581015963, 32919.91338869578, 990769.4550832732, 2797641.236124042, 9.1356987921761E7,
    0.6455597171305802, 1.6191181978847613, 96.75937654880184, 968.37014555772, 5364.367810646487, 25256.223054149883, 552350.4244723112, 7832874.365537663, 3.1863973163119152E7,
    0.10090404912840023, 4.367724218516824, 86.78145529336071, 378.8407064237704, 552.4430963593541, 75103.96641615983, 408087.6074993657, 749475.4234848522, 7071462.208726686,
    0.49858713928408827, 7.976677359655544, 70.67183152812501, 334.63314714588944, 5828.820196122292, 93558.51145348336, 240828.73651367452, 5083261.952871212, 6.996913834657456E7,
    0.05766733840298621, 2.3829850608459004, 25.62166217122629, 795.1889293375151, 5283.063955312124, 35112.89395737921, 722243.737463617, 1623186.7052564952, 5.8720185390479915E7,
    0.8301985243334447, 0.09186980770288566, 27.615420207359197, 519.2501286302929, 7179.090550260221, 51822.40293881892, 153562.28228867007, 956331.7689312479, 7.867701880340531E7,
    0.21406119412226887, 3.633000764086395, 42.029195709171, 829.0552060504004, 4952.322447239552, 80974.52781430166, 508353.80634131597, 6028566.900412552, 3.696692255818624E7,
    0.0667790651568585, 0.2171463389722983, 59.631530141398656, 62.40698899908137, 3479.120116764667, 59186.041588734806, 784491.3502808744, 152908.8648056609, 1.6456301800596362E7,
    0.07114509274980585, 7.222927660369147, 47.78145964613613, 346.4725725716009, 8711.245239124723, 64206.95604600988, 533723.2200521912, 3765506.7577946098, 2.7017935978382003E7,
    0.7059293959463335, 4.597745164831579, 92.7031354458151, 202.54202913037622, 2005.248993778732, 77105.89240237899, 74625.00828143625, 5769766.561618968, 2.56007840755736E7,
    0.17153658182987375, 9.194308190354167, 61.57423229749478, 621.0412649399586, 8989.57901989862, 23569.13184924798, 53104.17956941394, 1322057.7025323932, 6.30091625382655E7,
    0.34204185832853495, 2.8753884118944506, 77.88315018017754, 195.1922646337807, 5947.277254594413, 74291.35050001621, 683232.265489217, 8398966.623115847, 7.793321904700032E7,
    0.7613016839487818, 8.915144974035547, 66.82469682308185, 204.87906080170237, 3237.2989167860264, 60157.80215602664, 202295.81371743145, 4887435.426697317, 7.75034084961344E7,
    0.34262147119007513, 7.017563891449701, 86.16254260982116, 515.1360251080412, 6644.1068479087835, 141.84197062018234, 318909.3622388289, 3114335.6004772414, 9476297.529409228,
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  0.4546240513463974, 7.2412894388442295, 80.2405489522725, 202.3208522788349, 9010.241649790905, 15831.199981729727, 531309.949082128, 1734741.7139118514, 2.0789443538786713E7,
  0.9586104400833017, 0.7878430645220802, 26.178356264833546, 505.1492703599485, 7668.003970652098, 70739.4070300143, 357665.7409231473, 1893174.8890332766, 2.0325765905483373E7,
  0.020679540461011503, 2.1915563639581546, 70.12486525793646, 391.7343533088753, 9309.50769294146, 58319.912803235806, 558790.8155746709, 9831947.358874168, 6.185806837762997E7,
  0.6190983873271858, 2.2613542359036174, 89.73677225801951, 207.55797334744864, 2147.4096321617308, 35172.00922646657, 271183.21683293657, 7853824.204167615, 9.348764100201744E7,
  0.013025458884437069, 7.800156914483863, 95.49548954245897, 745.5872408972042, 8692.977795475095, 58066.72551746107, 321935.1025631055, 7602339.219366643, 5.421737969610986E7,
  0.6142798727175306, 1.931103340266338, 32.95359106746062, 119.38019632356101, 9028.740420450813, 28963.855113810954, 772084.2351890462, 4081250.293076691, 7.749694386159009E7,
  0.46359990924661054, 9.214633622583762, 45.24938025198186, 663.7506500754604, 2471.1065137787914, 45229.33505081038, 873108.437346603, 2354989.2187745324, 5.603238417798476E7,
  0.6398855898805721, 7.8750220815525305, 12.651856088829739, 57.96196458152747, 8068.390571154274, 42610.96200094845, 493544.71755031723, 4035960.807065396, 2.1478558566186532E7,
  0.07146505824636484, 9.156270170622715, 22.670738723667448, 570.6268961263214, 6171.495099559854, 92474.08468774469, 639636.4538565299, 6339879.041895221, 8.682200957652383E7,
  0.5878867899565411, 9.69846458687588, 63.62438868984648, 686.3022315243095, 1151.9565100581563, 79749.67732335145, 351362.1936543919, 2202196.3408184685, 4.265650495371396E7,
  0.47914319208117306, 6.94931709228414, 75.69829443005571, 973.6105644651864, 854.5235324181277, 67013.6181317581, 178152.5250360465, 8842232.181659902, 8413699.250472762,
  0.3280602482617907, 6.130369391290266, 67.3782017774648, 158.89009025974886, 1646.0006511657998, 64288.32489517832, 350078.50194551115, 2709156.63710543, 3738290.444659986,
  0.32916130181423586, 7.282681183068513, 44.17243005324663, 253.48316425997308, 4142.389072651452, 16767.07953148696, 764182.089693008, 9523549.40473968, 2.7419031447913654E7*/
    };

    public static void main(String[] args)
        {
        System.err.println("Various tests of Kahan and standard summing on a built-in table of doubles:\n");
        double sum = 0;
        for(int i = 0; i < test.length; i++)
            sum += test[i];
        System.err.println("Standard Sum " + sum);
        sum = 0;
        for(int i = test.length - 1; i >= 0; i--)
            sum += test[i];
        System.err.println("Reverse Standard Sum " + sum);
        System.err.println("Kahan Sum " + kahanSum(test));
        double[] test2 = new double[test.length];
        for(int i = 0; i < test.length; i++)
            test2[test.length - i - 1] = test[i];
        System.err.println("Reverse Kahan Sum " + kahanSum(test2));
        Kahan kahan = new Kahan();
        for(int i = 0; i < test.length; i++)
            kahan.add(test[i]);
        System.err.println("Kahan Incremental Sum " + kahan.getSum());
        kahan = new Kahan();
        for(int i = test.length - 1; i >= 0; i--)
            kahan.add(test[i]);
        System.err.println("Reverse Kahan Incremental Sum " + kahan.getSum());
        }


    }
